One-Way ANOVA Exam Practice

[Pages:6]C8057 ( Research Met hods I I ) : One- Way ANOVA Exam Pract ice

One-W ay I ndependent ANOVA: Exam Pract ice Sheet

Qu e st ion s

Question 1 Students were given different drug treatm ents before revising for their exam s. Som e were given a m em ory drug, som e a placebo drug and som e no t reat m ent . The exam scores ( % ) are shown below for t he t hree different groups:

Mean Variance Grand Mean Grand Variance

Memory Drug

70 77 83 90 97 83.40 112.30

Placebo

37 43 50 57 63 50.00 109.00 50.00 892.14

No Treatment

3 10 17 23 30 16.60 112.30

? Carry out a one- way ANOVA by hand t o t est t he hypot hesis t hat t he t reat m ent s will have different effects.

? Can you suggest som e follow- up com parisons ( wit h weight s) ?

Question 2

A neuropsychologist was int erest ed in how Monkeys learn t o perform a t ask. The t ask was t o ret rieve a coconut from t he opposit e side of a river. 15 wild m onkeys were assigned t o one of three conditions: observing a m onkey (they watched another m onkey ret rieve the coconut by building a bridge across t he st ream ) , observing a hum an (t hey watched a hum an solve the task), banana reward (they were allowed to do what they wanted but every tim e they engaged in behaviour t hat facilit at ed solving t he t ask t hey were rewarded wit h a banana. Aft er learning t he m onkeys were required t o solve t he problem again and t he t im e t aken t o solve the problem was m easured.

Dr. Andy Field

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4/18/ 2007

C8057 ( Research Met hods I I ) : One- Way ANOVA Exam Pract ice

Mean Variance Grand Mean Grand Variance

Banana Reward

1 1 7 13 13 7.00 36.00

Observing Monkey

7 15 1 8 9 8.00 25.00

8.67 24.67

Observing Human

15 8 13 13 6 11.00 14.50

? Carry out a one- way ANOVA by hand t o t est t he hypot hesis t hat som e form s of learning are m ore successful t han ot hers.

? Can you suggest som e follow- up com parisons ( wit h weight s) ?

Question 3

The experim ent er in quest ion 2 repeat ed t he experim ent above but wit h different Monkeys who had been lab- reared ( and so had ident ical learning experiences prior t o t he experim ent) .

Mean Variance Grand Mean Grand Variance

Banana Reward

6 7 7 7 8 7.00 0.50

Observing Monkey

7 8 8 8 9 8.00 0.50 8.67 7.52

Observing Human

8 6 15 13 13 11.00 14.50

? Carry out a one- way ANOVA by hand t o t est t he hypot hesis t hat som e form s of learning are m ore successful t han ot hers.

? Not e t hat t he m eans of t he groups are t he sam e as Experim ent 1. Can you explain any differences in t he result s bet ween t his experim ent and t he one in quest ion 2?

Question 4

A psychologist was int erest ed in whet her different TV shows lead t o a m ore posit ive out look on life. People were split int o 4 groups and t hen t aken t o a room t o view a program . The four groups saw: The Muppet Show, Fut uram a, The News, No program . Aft er t he program a blood sam ple was taken and serotonin levels m easured (rem em ber m ore serotonin m eans m ore happy!

Dr. Andy Field

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4/18/ 2007

C8057 ( Research Met hods I I ) : One- Way ANOVA Exam Pract ice

The Muppet Show

11 7 8 14 11 10 5

Mean

9.43

Variance

8.95

Grand Mean

Grand Variance

Futurama

4 8 6 11 9 8

7.67 5.87

BBC News

4 3 2 2 3 6

3.33 2.27 6.30 10.06

No Program

7 7 5 4 3 4 4 4 4.75 2.21

? Carry out a one- way ANOVA by hand t o t est t he hypot hesis t hat som e TV shows m ake people happier than ot hers.

? Can you suggest som e follow- up com parisons ( wit h weight s) ?

Dr. Andy Field

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4/18/ 2007

C8057 ( Research Met hods I I ) : One- Way ANOVA Exam Pract ice

Answ ers

Answ er to Question 1

Exam Score (%)

Memory Drug Placebo No Treatment Total

N 5 5 5

15

Descriptives

Mean 83.4000 50.0000 16.6000 50.0000

Std. Deviation

10.5972 10.4403 10.5972 29.8688

Std. Error 4.7392 4.6690 4.7392 7.7121

95% Confidence Interval for Mean

Lower Bound 70.2419

Upper Bound 96.5581

37.0366

62.9634

3.4419

29.7581

33.4592

66.5408

Minimum 70.00 37.00 3.00 3.00

Maximum 97.00 63.00 30.00 97.00

Exam Score (%)

Between Groups Within Groups Total

Sum of Squares 11155.600

1334.400

12490.000

ANOVA

df 2

12 14

Mean Square 5577.800 111.200

F 50.160

Sig. .000

Cont rast s would be ( weight s in bracket s) :

? Cont r a st 1 : { Mem ory Drug ( - 2) } vs. { Placebo ( 1) and No Treat m ent ( 1) }

? Cont r a st 2 : { Placebo ( - 1) } vs. { No Treat m ent ( 1) } -- [ Mem ory Drug would have a weight of 0 in this contrast]

Answ er to Question 2

Experiment 1

Banana Reward Observing Monkey Observing Human Total

N 5 5 5 15

Descriptives

Mean 7.0000 8.0000 11.0000 8.6667

Std. Deviation

6.0000 5.0000 3.8079 4.9666

Std. Error 2.6833 2.2361 1.7029 1.2824

95% Confidence Interval for Mean

Lower Bound -.4500

Upper Bound 14.4500

1.7917

14.2083

6.2719

15.7281

5.9163

11.4171

Minimum 1.00 1.00 6.00 1.00

Maximum 13.00 15.00 15.00 15.00

Experiment 1

Between Groups Within Groups Total

Sum of Squares

43.333

302.000

345.333

ANOVA

df 2

12 14

Mean Square 21.667 25.167

F .861

Sig. .447

Dr. Andy Field

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C8057 ( Research Met hods I I ) : One- Way ANOVA Exam Pract ice

There are no cont rol groups, so t here is no real correct way t o define cont rast s. However, you m ight want to first com bine observat ional learning condit ions and com pare with the reward learning (weights in brackets) :

? Cont r a st 1 : { Banana r eward ( - 2) } vs. { Observe Monkey ( 1) and Observe Hum an ( 1) } ? Cont r a st 2 : { Observe m onkey ( - 1) } vs. { Observe Hum an ( 1) } -- [ Banana Reward

would have a weight of 0 in this contrast]

Answ er to Question 3

Experiment 2

Banana Reward Observing Monkey Observing Human Total

N 5 5 5

15

Descriptives

Mean 7.0000 8.0000

11.0000 8.6667

Std. Deviation

.7071 .7071 3.8079 2.7430

Std. Error .3162 .3162

1.7029 .7082

95% Confidence Interval for Mean

Lower Bound 6.1220

Upper Bound 7.8780

7.1220

8.8780

6.2719

15.7281

7.1477

10.1857

Minimum 6.00 7.00 6.00 6.00

Maximum 8.00 9.00

15.00 15.00

Experiment 2

Between Groups Within Groups Total

Sum of Squares

43.333

62.000

105.333

ANOVA

df 2

12 14

Mean Square 21.667 5.167

F 4.194

Sig. .042

? The reason why t his ANOVA is significant whereas t he one in quest ion 2 is not is because t he variance wit hin groups is m uch sm aller (note the standard deviations in each group com pared t o quest ion 2 in t he t able of descript ives) . By using lab-reared m onkeys, thus cont rolling t he prior experiences of t he m onkeys, t he experim ent er has reduced t he variabilit y in t ask perform ance bet ween m onkeys wit hin a group. The result is t hat t he error variance is m uch lower ( not e in t he ANOVA t ables t hat t he SSMs ( bet ween group SS) are t he sam e but t he SSRs ( wit hin group SS) are different . Therefore, t he error against which t he experim ent al effect is t est ed is m uch lower.

Answ ers to Question 4

Serotonin Level

The Muppet Show Futurama BBC News No Program (Control) Total

N 7 6 6 8 27

Descriptives

Mean 9.4286 7.6667 3.3333 4.7500 6.2963

Std. Deviation

2.9921 2.4221 1.5055 1.4880 3.1722

Std. Error 1.1309 .9888 .6146 .5261 .6105

95% Confidence Interval for Mean

Lower Bound 6.6614

Upper Bound 12.1958

5.1248

10.2085

1.7534

4.9133

3.5060

5.9940

5.0414

7.5512

Minimum 5.00 4.00 2.00 3.00 2.00

Maximum 14.00 11.00 6.00 7.00 14.00

Dr. Andy Field

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4/18/ 2007

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